The first of these works concerned the one loop divergences in
quantum GR coupled to quantum matter. Already in the first paper
with one-loop calculations, 't Hooft and Veltman derived also the
divergences for QG coupled to the minimal scalar field [1]}.
It is interesting that the case of quantum GR coupled to the
nonminimal quantum scalar \(\phi \)  (nonminimal means the presence
of the term \(\xi R\phi ^2\) ) can be reduced to the calculations with
a minimal scalar by the change of variables, i.e., the conformal
transformation [2]}. However, the correspondence with the
direct calculation [3]} required much greater effort and was
achieved only two decades later in [4]}. This example shows
importance and complications related to the choice of parametrization.
The calculations in gravity-vector (Abelian and nonabelian) and
gravity-fermion models were done almost at the same time as
[1]} by Deser, van Nieuwenhuisen et al in [6]}. Let
us note that more general combinations of
quantum fields including QG were explored in supergravity, but
since there is a special Section of this Handbook about supergravity,
we do not need to discuss this part here. The important general
result of the mentioned calculations is that, for matter-gravity
systems, the one-loop divergences do not vanish on shell
[1]}, [6]}.
